Given the pop, I'd say its unlikely, but do what Saffith said, and hopefully it'll work out. If it's happened repeatedly (I wouldn't recommend checking, but if you tried it repeatedly and it happened the same each time) then there may be more of a chance, but again, I wouldn't be too hopeful )
If not, you might be able to get some of the data out. I imagine Nintendo has some way in place for you to be able to log in with your current account on a new device if need be (which should at least save some money if you bought any digital stuff). Any solid storage (game cartridges and SD cards) should be fine, and I don't believe the 2DS uses any moving parts for its data storage, so you might be able to get it taken out and put in a new one (although I don't know how companies are with stuff like that - it might void a warranty or something).
I lost my DS lite to a milk spillage by my mum a few years ago, so I hope things go well for your 2DS.